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Unformatted text preview: ve constant returns? Interpret constant returns.
The long run production function was . In the short run, capital is fixed so that . This yields the short
9 ECO 204 Chapter 13: Practice Problems & Solutions for The Short Run Cost Minimization Problem in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. run production function: Let’s assume k = 100 Observe that Elasticity of q with respect to L = % Change in q / % Change in L is
)( ( ) ) Thus Or % Change in q = α (% Change in L)
For constant returns (“doubling variable input doubling output”) we would need α = 1. In this case, the short run
production function becomes:
which is a linear production function.
Observe the contrast between the long and short runs • In the long run, doubling all inputs will double output when
• In the short run, doubling the variable input will double output when
It is important not to confuse RTS with returns. These are two entirely different concepts. More crucially, even if there
are constant returns to scale, that does not mean there are constant.
(b) For a given value of α, what is Ajax’s short run demand for labor?
We showed that given the short run production function q = f(L, k) (note how I am using “k” not “K” to denote the fact
that capital is fixed at the level “k”), we can solve for the optimal L as
) ( ) Note that if there are constant returns (α = 1) then L = q/10 so that if q doubles, we must also double labor.
ECO 204 Chapter 13: Practice Problems & Solutions for The Short Run Cost Minimization Problem in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (c) For a given value of α, what is Ajax’s sho...
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This document was uploaded on 01/19/2014.
- Fall '14